Question

raja invested Rs.2000 in bank for 3 years and get RS. 315.25 as interest which was compounded annually. Find the rate of interest offered.

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Answer 1

Answer:

$\large{\underline{\boxed{\mathfrak\green{Rate \: of \: interest = 5\%}}}}$

$\rule{100}{2}$

Question:-

Raja invested Rs.2000 in bank for 3 years and get Rs.315.25 as interest which was compounded annually.Find the rate of interest offered.

Solution:-

Given:-

• Principal (p) = Rs.2000
• Time(n) = 3 years.
• Compound interest (CI) = Rs.315.25

To find:-

• Rate of interest (r) = ?

We know,

$\star\: \: {\boxed{\sf\green{CI = P(1 + r)^n - P }}}$

• Putting values:-

⇒ 315.25 = 2000(1 + r)³ - 2000

⇒ 315.25 = 2000 × (1 + r)³ - 2000

⇒ 2000(1 + r)³ = 315.25 + 2000

⇒ 2000(1 + r)³ = 2315.25

⇒ (1 + r)³ = 2315.25/2000

⇒ (1 + r)³ = 1.157625

⇒ $\sf (1 + r) = 1.157625^ \frac{1}{3}$

⇒ 1 + r = 1.05

⇒ r = 1.05 - 1

⇒ r = 0.05

⇒ r = 5/100

⇒ r = 5%

$\therefore{\underline{\rm{Rate \: of \: interest \: offered = 5\%}}}$

Answer 2

Answer:

The rate is 5%

Step-by-step explanation:

Given :

Invested = Rs. 2000

For = 3 years

Got Interest of = Rs. 315.25

To find :

The rate of interest

Solution :

$\longrightarrow$ Amount = CI + P

$\longrightarrow$ 315.25 + 2000

$\longrightarrow$ 2315.25

________________________________

$\longrightarrow$ A = P (1 + R/100)^n

$\longrightarrow$ 2315.25 = 2000(1 + R/100)³

$\longrightarrow$ 2315.25/2000 = (1 + R/100)³

$\longrightarrow$ 9261/8000 = (1 + R/100)³

$\longrightarrow$ Cube root of 9261/8000 = (1 + R/100)

$\longrightarrow$ 21/20 = 1 + R/100

$\longrightarrow$ 21/20 = 100 + R/100

$\longrightarrow$ 21/20 × 100 = 100 + R

$\longrightarrow$ 105 = 100 + R

$\longrightarrow$ R = 105 - 100

$\longrightarrow$ R = 5 %

Therefore, The rate is 5%